Christiaan Huygens

In this paper it is shown the performing of an optical transform to state the scalar diffraction in the formulation of the wavelet transform and the 'wave equations'. From there, a bridge is build between equations of spherical waves presented in 1678 by Huygens and the continuous wavelet transform. For such a purpose, wavelets are introduced that meet the principles of waves and the properties of wavelets. The following equations are applied in solution to show a correspondence between the Huygens-Fresnel diffraction and the wavelet transform.

On the 2th October 2017, the Noble Prize in Physiology or Medicine was awarded to three researchers who were able to elucidate how the internal, biological clock of living organisms adapts itself so that it is synchronized with the Earth’s revolutions.
Christiaan Huygens (1629-1695) was the first physicist to observe and analyze the phenomenon of synchronization. More precisely, the Dutch physicist and astronomer observed on the 1st March of 1665  that two pendulum clocks which were standing in front of him started to move in phase. He couldn’t believe his eyes and tried to find a mechanical explanation for this spectacular observation “which no one ever would have thought of.“. Initially, he interpreted ‘l’accord merveilleux’ as a kind of ‘sympathy’ but already one month later he discovered the real mechanical cause of this odd phenomenon.
In this volume, Dr. Kurt Wiesenfeld explains how his research group has examined synchronization by means of reconstructions of Huygens’ pendulum clocks. In another paper, Dr. Filip Buyse argues that Spinoza was in contact with Christiaan Huygens during the period of his spectacular invention. Hence, the Dutch physicist and astronomer might have influenced and inspired Spinoza (1632 -1677) in his views on the agreement between bodies in the universe. This would resolve Spinoza’s otherwise paradoxical phrases in his answer to Robert Boyle’s question, in his Letter 32 (1665) to the secretary of the Royale Society.  Furthermore, Dr. Maxime Rovere argues in his paper that Spinoza might also have been influenced by the physics of oscillating pendulums in his theory of emotions. 
Christiaan Huygens designed his pendulum clock in 1656 and it was built by his instrument maker Salomon Coster (ca.1622-1659). He patented his sophisticated machine in 1657. However, Huygens was not the first to conceive a pendulum regulated clock. As he reveals in his Horologium (1658), his invention was based on Galileo’s invention of the principle of isochronism. (A principle which is discussed by Dr. Mohammed Abattouy in this special issue.) There is historical evidence that Galileo had already started to do research on the movement of a pendulum in 1603. At that moment he was professor in Padua. In this issue, Fabrizio Bigotti and David Taylor reconstruct and discuss a seventeenthth century medical instrument designed based on the pendulum. This pulsilogium was probably invented by one of Galileo’s colleagues, Santorio Santorio (1561-1636).  .....

There is no need to argue for the relevance of affectivity in early modern philosophy. When doing research and conceptualizing affectivity in this period, we hope to attain a basic interpretive framework for philosophy in general, one that is independent of and cutting across such unfruitful divisions as the time-honored interpretive distinction between “rationalists” and “empiricists”, which we consider untenable when applied to 17th-century thinkers.
Our volume consists of papers based on the contributions to the First Budapest Seminar in Early Modern Philosophy, held on 14-15 October 2016 at Eötvös Loránd University, Budapest. When composing this volume, our aim was not to present a systematic survey of affectivity in early modern philosophy. Rather, our more modest goal was to foster collaboration among researchers working in different countries and different traditions. Many of the papers published here are already in implicit or explicit dialogue with others. We hope that they will generate more of an exchange of ideas in the broader field of early modern scholarship.

The mathematical nature of modern science is an outcome of a contingent historical process, whose most critical stages occurred in the seventeenth century. 'The mathematization of nature' (Koyré 1957, From the closed world to the infinite universe, 5) is commonly hailed as the great achievement of the 'scientific revolution', but for the agents affecting this development it was not a clear insight into the structure of the universe or into the proper way of studying it. Rather, it was a deliberate project of great intellectual promise, but fraught with excruciating technical challenges and unsettling epistemological conundrums. These required a radical change in the relations between mathematics, order and physical phenomena and the development of new practices of tracing and analyzing motion. This essay presents a series of discrete moments in this process. For mediaeval and Renaissance philosophers, mathematicians and painters , physical motion was the paradigm of change, hence of disorder, and ipso facto available to mathematical analysis only as idealized abstraction. Kepler and Galileo boldly reverted the traditional presumptions: for them, mathematical harmonies were embedded in creation; motion was the carrier of order; and the objects of mathematics were mathematical curves drawn by nature itself. Mathematics could thus be assigned an explanatory role in natural philosophy, capturing a new metaphysical entity: pure motion. Successive generations of natural philosophers from Descartes to Huygens and Hooke gradually relegated the need to legitimize the application of mathematics to natural phenomena and the blurring of natural and artificial this application relied on. Newton finally erased the distinction between nature's and artificial mathematics altogether, equating all of geometry with mechanical practice.