A SCHOLARLY BOOK REPOSITORY10 start with B start with B
Gal and Chen-Morris show how the protagonists of the new mathematical natural philosophy grasped at the very far and very small by entrusting observation to the mediation of artificial instruments, and how they justified this mediation by naturalizing and denigrating the human senses. They show how the physical-mathematical ordering of heavens and earth demanded obscure and spurious mathematical procedures, replacing the divine harmonies of the late Renaissance with an assemblage of isolated, contingent laws and approximated constants. Finally, they show how the new savants, forced to contend that reason is hopelessly estranged from its surrounding world and that nature is irreducibly complex, turned to the passions to provide an alternative, naturalized foundation for their epistemology and ethics.
Enforcing order in the face of threatening chaos, blurring the boundaries of the natural and the artificial, and mobilizing the passions in the service of objective knowledge, the New Science, Gal and Chen-Morris reveal, is a Baroque phenomenon: deeply entrenched in and crucially formative of the culture of its time.
Before Voltaire explores how Newton’s ideas made their way not just through the realm of French science, but into the larger world of society and culture of which Principia was an intertwined part. Shank also details a history of the beginnings of calculus-based mathematical physics that integrates it into the larger intellectual currents in France at the time, including the Battle of the Ancients and the Moderns, the emergence of wider audiences for science, and the role of the newly reorganized Royal Academy of Sciences. The resulting book offers an unprecedented cultural history of one the most important and influential elements of Enlightenment science.
Jesseph begins with Berkeley's radical opposition to the received view of mathematics in the philosophy of the late seventeenth and early eighteenth centuries, when mathematics was considered a "science of abstractions." Since this view seriously conflicted with Berkeley's critique of abstract ideas, Jesseph contends that he was forced to come up with a nonabstract philosophy of mathematics. Jesseph examines Berkeley's unique treatments of geometry and arithmetic and his famous critique of the calculus in The Analyst.
By putting Berkeley's mathematical writings in the perspective of his larger philosophical project and examining their impact on eighteenth-century British mathematics, Jesseph makes a major contribution to philosophy and to the history and philosophy of science.
Optimists believe this is the best of all possible worlds. And pessimists fear that might really be the case. But what is the best of all possible worlds? How do we define it? Is it the world that operates the most efficiently? Or the one in which most people are comfortable and content? Questions such as these have preoccupied philosophers and theologians for ages, but there was a time, during the seventeenth and eighteenth centuries, when scientists and mathematicians felt they could provide the answer.
This book is their story. Ivar Ekeland here takes the reader on a journey through scientific attempts to envision the best of all possible worlds. He begins with the French physicist Maupertuis, whose least action principle asserted that everything in nature occurs in the way that requires the least possible action. This idea, Ekeland shows, was a pivotal breakthrough in mathematics, because it was the first expression of the concept of optimization, or the creation of systems that are the most efficient or functional. Although the least action principle was later elaborated on and overshadowed by the theories of Leonhard Euler and Gottfried Leibniz, the concept of optimization that emerged from it is an important one that touches virtually every scientific discipline today.
Tracing the profound impact of optimization and the unexpected ways in which it has influenced the study of mathematics, biology, economics, and even politics, Ekeland reveals throughout how the idea of optimization has driven some of our greatest intellectual breakthroughs. The result is a dazzling display of erudition—one that will be essential reading for popular-science buffs and historians of science alike.
Although largely unknown today, during his lifetime Mutio Oddi of Urbino (1569–1639) was a highly esteemed scholar, teacher, and practitioner of a wide range of disciplines related to mathematics. A prime example of the artisan-scholar so prevalent in the late Renaissance, Oddi was also accomplished in the fields of civil and military architecture and the design and retail of mathematical instruments, as well as writing and publishing.
In Between Raphael and Galileo, Alexander Marr resurrects the career and achievements of Oddi in order to examine the ways in which mathematics, material culture, and the book shaped knowledge, society, and the visual arts in late Renaissance Italy. Marr scrutinizes the extensive archive of Oddi papers, documenting Oddi’s collaboration with prominent intellectuals and officials and shedding new light on the practice of science and art during his day. What becomes clear is that Oddi, precisely because he was not spectacularly innovative and did not attain the status of a hero in modern science, is characteristic of the majority of scientific practitioners and educators active in this formative age, particularly those whose energetic popularization of mathematics laid the foundations for the Scientific Revolution. Marr also demonstrates that scientific change in this era was multivalent and contested, governed as much by friendship as by principle and determined as much by places as by purpose.
Plunging the reader into Oddi’s world, Between Raphael and Galileo is a finely wrought and meticulously researched tale of science, art, commerce, and society in the late sixteenth and early seventeenth century. It will become required reading for any scholar interested in the history of science, visual art, and print culture of the Early Modern period.
Caws takes us back to Pascal’s youth, when he was a child prodigy first engaging mathematics through the works of mathematicians such as Father Mersenne. She describes his early scientific experiments and his construction of mechanical calculating machines; she looks at his correspondence with important thinkers such as René Descartes and Pierre de Fermat; she surveys his many inventions, such as the first means of public transportation in Paris; and she considers his later religious exaltations in works such as the “Memorial.” Along the way, Caws examines Pascal’s various modes of writing—whether he is arguing with the strict puritanical modes of church politics, assuming the personality of a naïve provincial trying to understand the Jesuitical approach, offering pithy aphorisms in the Pensées, or meditating on thinking about thinking itself.
Altogether, this book lays side by side many aspects of Pascal’s life and work that are seldom found in a single volume: his religious motivations and faith, his scientific passions, and his practical savvy. The result is a comprehensive but easily approachable account of a fascinating and influential figure.
"Ivar Ekeland gained a large and enthusiastic following with Mathematics and the Unexpected, a brilliant and charming exposition of fundamental new discoveries in the theory of dynamical systems. The Broken Dice continues the same theme, and in the same elegant, seemingly effortless style, but focuses more closely on the implications of those discoveries for the rest of human culture. What are chance and probability? How has our thinking about them been changed by the discovery of chaos? What are all of these concepts good for? . . . Ah, but, I mustn't give the game away, any more than I should if I were reviewing a detective novel. And this is just as gripping a tale. . . . Beg, borrow, or preferably buy a copy. . . . I guarantee you won't be disappointed."—Ian Stewart, Science
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