Julie Taymor is an exemplary artist who has successfully made the transition from avant-garde director of live theatre in the 1980s to become a Broadway director for Disney Corporation with The Lion King, and, more recently, a film director with Sony’s nostalgic look at the music of the Beatles in Across the Universe. Highlights of her career—spanning the latter half of the twentieth century—offer excellent examples of the changes in the economics of creativity and artistic labor for a case study (...) in cultural and aesthetic values under global capitalism. Through interviews, newspapers and financial annual reports, specific moments in Taymor’s oeuvre reveal key distinctions between cultural and intercultural values, between aesthetic and financial exchange values, and highlight themes and limitations in the legacy of the Marxist labor theory of value. (shrink)

Progressive supranuclear palsy is a movement disorder with prominent tau neuropathology. Brain diseases with abnormal tau deposits are called tauopathies, the most common of which is Alzheimer's disease. Environmental causes of tauopathies include repetitive head trauma associated with some sports. To identify common genetic variation contributing to risk for tauopathies, we carried out a genome-wide association study of 1,114 individuals with PSP and 3,247 controls followed by a second stage in which we genotyped 1,051 cases and 3,560 controls for the (...) stage 1 SNPs that yielded P ≤ 10-3. We found significant previously unidentified signals associated with PSP risk at STX6, EIF2AK3 and MOBP. We confirmed two independent variants in MAPT affecting risk for PSP, one of which influences MAPT brain expression. The genes implicated encode proteins for vesicle-membrane fusion at the Golgi-endosomal interface, for the endoplasmic reticulum unfolded protein response and for a myelin structural component. © 2011 Nature America, Inc. All rights reserved. (shrink)

Ḥelek 2. Toroto shel Rabenu bi-lesh. ha-ḳ. ... maʼamarim shonim be-Idish ... sheʼelot u-teshuvot ba-ʻavodat ha-Sh. yit ... shivḥo shel tsadiḳ.

We apply Benacerraf’s distinction between mathematical ontology and mathematical practice to examine contrasting interpretations of infinitesimal mathematics of the seventeenth and eighteenth century, in the work of Bos, Ferraro, Laugwitz, and others. We detect Weierstrass’s ghost behind some of the received historiography on Euler’s infinitesimal mathematics, as when Ferraro proposes to understand Euler in terms of a Weierstrassian notion of limit and Fraser declares classical analysis to be a “primary point of reference for understanding the eighteenth-century theories.” Meanwhile, scholars like (...) Bos and Laugwitz seek to explore Eulerian methodology, practice, and procedures in a way more faithful to Euler’s own. Euler’s use of infinite integers and the associated infinite products are analyzed in the context of his infinite product decomposition for the sine function. Euler’s principle of cancellation is compared to the Leibnizian transcendental law of homogeneity. The Leibnizian law of continuity similarly finds echoes in Euler. We argue that Ferraro’s assumption that Euler worked with a classical notion of quantity is symptomatic of a post-Weierstrassian placement of Euler in the Archimedean track for the development of analysis, as well as a blurring of the distinction between the dual tracks noted by Bos. Interpreting Euler in an Archimedean conceptual framework obscures important aspects of Euler’s work. Such a framework is profitably replaced by a syntactically more versatile modern infinitesimal framework that provides better proxies for his inferential moves. (shrink)

Did Leibniz exploit infinitesimals and infinities à la rigueur or only as shorthand for quantified propositions that refer to ordinary Archimedean magnitudes? Hidé Ishiguro defends the latter position, which she reformulates in terms of Russellian logical fictions. Ishiguro does not explain how to reconcile this interpretation with Leibniz’s repeated assertions that infinitesimals violate the Archimedean property (i.e., Euclid’s Elements, V.4). We present textual evidence from Leibniz, as well as historical evidence from the early decades of the calculus, to undermine Ishiguro’s (...) interpretation. Leibniz frequently writes that his infinitesimals are useful fictions, and we agree, but we show that it is best not to understand them as logical fictions; instead, they are better understood as pure fictions. (shrink)

Abraham Robinson’s framework for modern infinitesimals was developed half a century ago. It enables a re-evaluation of the procedures of the pioneers of mathematical analysis. Their procedures have been often viewed through the lens of the success of the Weierstrassian foundations. We propose a view without passing through the lens, by means of proxies for such procedures in the modern theory of infinitesimals. The real accomplishments of calculus and analysis had been based primarily on the elaboration of novel techniques for (...) solving problems rather than a quest for ultimate foundations. It may be hopeless to interpret historical foundations in terms of a punctiform continuum, but arguably it is possible to interpret historical techniques and procedures in terms of modern ones. Our proposed formalisations do not mean that Fermat, Gregory, Leibniz, Euler, and Cauchy were pre-Robinsonians, but rather indicate that Robinson’s framework is more helpful in understanding their procedures than a Weierstrassian framework. (shrink)

In relation to a thesis put forward by Marx Wartofsky, we seek to show that a historiography of mathematics requires an analysis of the ontology of the part of mathematics under scrutiny. Following Ian Hacking, we point out that in the history of mathematics the amount of contingency is larger than is usually thought. As a case study, we analyze the historians’ approach to interpreting James Gregory’s expression ultimate terms in his paper attempting to prove the irrationality of \. Here (...) Gregory referred to the last or ultimate terms of a series. More broadly, we analyze the following questions: which modern framework is more appropriate for interpreting the procedures at work in texts from the early history of infinitesimal analysis? As well as the related question: what is a logical theory that is close to something early modern mathematicians could have used when studying infinite series and quadrature problems? We argue that what has been routinely viewed from the viewpoint of classical analysis as an example of an “unrigorous” practice, in fact finds close procedural proxies in modern infinitesimal theories. We analyze a mix of social and religious reasons that had led to the suppression of both the religious order of Gregory’s teacher degli Angeli, and Gregory’s books at Venice, in the late 1660s. (shrink)

Ḥeshbonot -- ʻEtsot maʻásiyot -- Harḥaḳot.

ha-Musar shebe-ḥayim -- ʻOleh, yored ṿe-ʻoleh -- Maʼamarim u-derashot ʻal ʻinyanim aḳṭuʼaliyim.

Cauchy's sum theorem is a prototype of what is today a basic result on the convergence of a series of functions in undergraduate analysis. We seek to interpret Cauchy’s proof, and discuss the related epistemological questions involved in comparing distinct interpretive paradigms. Cauchy’s proof is often interpreted in the modern framework of a Weierstrassian paradigm. We analyze Cauchy’s proof closely and show that it finds closer proxies in a different modern framework.

To explore the extent of embeddability of Leibnizian infinitesimal calculus in first-order logic (FOL) and modern frameworks, we propose to set aside ontological issues and focus on pro- cedural questions. This would enable an account of Leibnizian procedures in a framework limited to FOL with a small number of additional ingredients such as the relation of infinite proximity. If, as we argue here, first order logic is indeed suitable for developing modern proxies for the inferential moves found in Leibnizian infinitesimal (...) calculus, then modern infinitesimal frameworks are more appropriate to interpreting Leibnizian infinitesimal calculus than modern Weierstrassian ones. (shrink)

Diese Abhandlung von 1748 fand unter den Zeitgenossen endlich die große und ungeteilte Beachtung, die Hume für seine kritischen Untersuchungen zur dogmatischen und empirischen Erkenntnis erwarten durfte. Seit Kants Bekenntnis, er sei durch diesen Text aus einem "dogmatischen Schlummer" erweckt und zu seinen eigenen kritischen Untersuchungen bewegt worden, gilt das Buch als Humes bedeutendstes Hauptwerk.

Jon Elster reports that in 1940, and again in 1970, the U.S. draft lottery was challenged for falling short of the legally mandated ‘random selection’. On both occasions, the physical mixing of the lots appeared to be incomplete, since the birth dates were clustered in a way that would have been extremely unlikely if the lots were fully mixed. There appears to have been no suspicion on either occasion that the deficiency in the mixing was intended, known, or believed to (...) favor or disfavor any identifiable group. If the selection was non-random in the way charged, Elster asks, was it unfair? (shrink)