Seventeenth-century optics naturalizes the eye while estranging the mind from objects. A mere screen, on which rests a blurry array of light stains, the eye no longer furnishes the observer with genuine re-presentations of visible objects. The intellect is thus compelled to decipher flat images of no inherent epistemic value, accidental effects of a purely causal process, as vague, reversed reflections of wholly independent objects. Reflecting on and trespassing the boundaries between natural and artificial, orderly and disorderly, this optical paradox (...) is a Baroque phenomenon; and it is the origin of Descartes’ celebrated doubt---whether we know anything at all. (shrink)

A major intellectual shift between Copernicus and the mid-17th century was the rejection of Aristotelian assertions concerning the relationship of mathematics to physical nature. Aristotle asserted that “The minute accuracy of mathematics is not to be demanded in all cases, but only in the case of things which have no matter. Therefore its method is not that of natural science; for presumably all nature has matter.” Thus, he pulled out the rug from under the feet of the aspiration to a (...) mathematically based natural sciences, asserting that: “And at the same time not even this is true, that mensuration deals with perceptible and perishable magnitudes; for then it would have perished, when they perished. And astronomy also cannot be dealing with perceptible magnitudes nor with this heaven above us. For neither are perceptible lines such lines as the geometer speaks of, nor are the movement and complex orbits in the heaven like those which astronomy treats, nor have geometrical points the same nature as the actual stars.”. (shrink)

The following paper, together with its sequel ("The use and non-use of mathematics"), is a study in the mathematization of nature. It looks into the history of one of the most emblematic achievements of this fundamental aspect of the making of modem science - the Inverse Square Law of universal gravitation - before its celebrated application by Newton to celestial mechanics. What did it take, we ask, to tum a particular mathematical ratio into a candidate for a law of nature?

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. (shrink)

The following is the second part of our Archaeology of the Inverse Square Law. Together these papers examine the transformation of the inverse square ratio from its origins in a metaphysical image of medieval thought in Grosseteste and the perspectivist tradition, through a playful magical practice in the Renaissance with Cusanus and Dee, and into a mathematical tool, applicable to the physical world. This last transformation allowed Newton to condense the geometrical image into a celebrated algebraic equation for universal gravity, (...) but it proved particularly confusing for the people who wrought it, Kepler and Hooke. (shrink)

Kepler's Somnium is a fantastical story about the world on the moon. It presents a heliocentric world-picture established through a total conversion of the meaning and place of observation in the hierarchy of knowledge. This epistemological program is construed through a critical adaptation of Lucian's "True Story," and Plutarch's "The Face on the Moon." Utilizing his new optics, embodied in the Camera obscura, Kepler inverts the meaning of these classical texts together with the reader's point of view. Astronomical knowledge is (...) vindicated and scientific observation is the only way out of an obscure and mannerist dream. (shrink)