Galileo's legacy: a critical edition and translation of the manuscript of Vincenzo Viviani's Grati Animi Monumenta.
Having been found 'vehemently suspected of heresy' by the Holy Office in 1633, at the time of his death (1642) Galileo's remains were laid to rest in the tiny vestry of a lateral chapel of the Santa Croce Basilica, Florence. Throughout his life, Vincenzo Viviani, Galileo's last disciple, struggled to have his master's name rehabilitated and his banned works reprinted, as well as a proper funeral monument erected. He did not live to see all this come true, but his efforts triggered a mechanism that eventually led to the fulfilment of his wishes. A key element of his project was the transformation of the facade of his palace into a private (but publicly rendered) tribute to Galileo, with two long inscriptions celebrating Galileo's achievements and calling Florence's attention to the need to pay a proper tribute to him. Shortly afterwards, he revised the text and circulated it in print. This article presents the first critical edition and annotated translation of Viviani's original manuscript, long thought to be lost, and describes its role in Viviani's lifelong struggle for Galileo's intellectual legacy, as well as its impact on future historiography.
European Longitude Prizes. III. The Unsolved Mystery of an Alleged Venetian Longitude Prize
Despite frequent references in modern reviews to a seventeenth-century Venetian longitude prize, only a single, circumstantial reference to the alleged prize is known from contemporary sources. Edward Harrison’s scathing assessment of the conditions governing the award of an alleged Venetian longitude prize simultaneously disparages the rewards offered by the Dutch States General. However, the latter had long run its course by 1696, the year of the citation, thus rendering Harrison’s reference unreliable. Whereas other longitude awards offered by the leading European maritime nations attracted applicants from far and wide, often accompanied by extensive, self-published pamphlets, the alleged Venetian prize does not seem to have been subject to similar hype. The alleged existence of seventeenth-century Venetian award is particularly curious, because the city’s fortune was clearly in decline, and longitude determination on the open seas does not appear to have been a priority; the city’s mariners already had access to excellent ‘portolan’ charts. It is therefore recommended that authors refrain from referring to a potentially phantom Venetian longitude prize in the same context as the major sixteenthto eighteenth-century European awards offered by the dominant sea-faring nations.
The quantum particle in a box: what we can learn from classical electrodynamics
The problem of a charged particle enclosed in an infinite square potential well is analysed from the point of view of classical theory with the addition of the electromagnetic zero-point radiation field, with the aim to explore the extent to which such an analysis can contribute to enhance our understanding of the quantum behavior. First a proper treatment is made of the freely moving particle subject to the action of the radiation field, involving a frequency cutoff ωc. The jittering motion and the effective structure of the particle are sustained by the permanent action of the zero-point field. As a result, the particle interacts resonantly with the traveling field modes of frequency ωc in its proper frame of reference, which superpose to give rise to a modulated wave accompanying the particle. This is identified with the de Broglie wave, validating the choice of Compton’s frequency for ωc. For the stationary states of particles confined in the potential well, the Lorentz force produced by the accompanying field is shown to lead to discrete values for the mean speed and to an uneven probability distribution that echoes the corresponding quantum distribution. The relevance of the results obtained and the limitations of the classical approach used, are discussed in the context of present-day stochastic electrodynamics.