Tag Archives: Descartes

A brief history of space (3/4) : from Descartes to Schwarzschild

Sequel of the preceding post A Brief History of Space (2/4) : From Ptolemy to Galileo

At the beginning of XVIIth century, the way was open for new cosmologies, constructed on the basis of infinite space. Until then, the notion of space was conceived in the cosmological and physical order of nature, and not as the “background” of the figures and geometric constructions of Euclid. In other terms, physical space was not mathematicized. It became so thanks to René Descartes (1596 – 1650), who had the idea of specifying each point by three real numbers: its coordinates. The introduction of a universal system of coordinates which entirely criss-crossed space and allowed for the measurement of distances was a reflection of the fact that, for Descartes, the unification and uniformization of the universe in its physical content and its geometric laws was a given. Space is a substance in the same class as material bodies, an infinite ether agitated by vortices without number, at the centers of which were held the stars and their planetary systems.

A portrait of René Descartes

This new conception of the cosmos upset philosophical thought and led it far from the initial enthusiasm of the atomists and Giordano Bruno: “The absolute space which inspired the hexameters of Lucretius, the absolute space which that had been a liberation for Bruno, was a labyrinth and an abyss for Pascal.”[5] As for the scholars, they did not allow themselves to be discouraged by these moods and irresistibly moved towards the infinite universe.

The Descartes system of the world using vortices

The tendency toward the radical geometrization of an infinite space, initiated by Descartes, was consummated by the Englishman Isaac Newton (1642-1727). Newton postulated an absolute space, encompassing not only the background space of mathematics and the physical space of astronomy, but also that of metaphysics, since space was the “sensorium of God.” Physical space, finally identified with geometrical space, was necessarily Euclidean (the only one known at the epoch), without curvature, amorphous and infinite in every direction. At the heart of this immobile framework, Newton explained celestial mechanics in terms of the law of universal attraction, from now on considered responsible for gravitation and the large scale structure of the Universe. With Newton, cosmology took root for more than two centuries in the framework of an infinite Euclidean space and an eternal time.

Newton around 1700

All the problems are not resolved in Newtonian cosmology, far from it. On the question of the distribution of stars in space, for example, Newton believed that they must occupy a finite volume since, he argued, if they occupied an infinite space, they would be infinite in number, the force of gravitation would be infinite, and the universe would be unstable. Newton moreover supposed that the stars were uniformly spread within a finite mass|like a galaxy, for example. But a problem of instability remained: since each celestial body is attracted by every other one, at the least movement, at the least mechanical perturbation, all the bodies in the universe would fall towards a unique center, and the universe would collapse. Newton’s universe is therefore only viable if it does not admit motion on the large scale: its space is rigid and its time immobile. Continue reading

Cosmogenesis (8) : The Nebular Hypothesis

Sequel of the preceding post Cosmogenesis (7) : The Date of the Creation

The Nebular Hypothesis

The ancient Babylonians had a different idea of how the world began. They believed that it had evolved rather than being created instantaneously. Assyrian inscriptions have been found which suggest that the cosmos evolved after the Great Flood and that the animal kingdom originated from earth and water. This idea was at least partially incorporated into a monotheist doctrine and found its way into the sacred texts of the Jews, neighbors and disciples of the Babylonians. It was also taken up by the early Ionian philosophers, including Anaximander and Anaximenes, and by the Stoics and atomists.

A portrait of Democritus (460-370 BC), the founder of atomistic theory.
A portrait of Democritus (460-370 BC), the founder of atomistic theory.

Democritus developed a theory that the world had originated from the void, a vast region in which atoms were swirling in a whirlpool or vortex. The heaviest matter was sucked into the center of the vortex and condensed to form the earth. The lightest matter was thrown to the outside where it revolved so rapidly that it eventually ignited to form the stars and planets. These celestial bodies, as well as the earth itself, were kept in position by centrifugal force. This concept admitted the possibility that the universe contained an infinite number of objects. It also anticipated the 19th century theory of the origin of the solar system, known as the nebular hypothesis, according to which a “primitive nebula” condensed to form the sun and planets.

The idea of universal evolution had a strong influence on classical thought and developed in various directions during Greek and Roman times. In the first century BC Lucretius extended the theories of atomism and evolution to cover every natural phenomenon[i] and argued that all living things originated from earth. Two centuries later, in his medical treatise On the Use of the Parts of the Body[ii], the Greek physician Galen (Claudius Galenus) expressed the essentially Stoic view that matter is eternal and that even God is subject to the laws of nature: contrary to the literal interpretation of the Genesis story, he could not have “formed man from the dust of the ground”; he could only have shaped the dust according to the laws governing the behaviour of matter. The Church Fathers, who insisted that the Creation was instantaneous, rejected any sort of evolutionary theory; to them the ideas of the Stoics and atomists were heretical.

In the second half of the 16th century the idea of universal evolution began to be incorporated into the new system of scientific thought resulting from the work of Copernicus, Kepler, Galileo, Descartes and Newton. According to Descartes, for example, space consisted of “whirlpools” of matter whose motion was governed by the laws of physics. Newton, with his theory of universal attraction, was accused of having substituted gravitation for providence, for having replaced God’s spiritual influence on the cosmos by a material mechanism[iii]. A new view of the world had nevertheless been established, whereby the workings of the universe were subject not to the whim of the Almighty but to the laws of physics – it was an irreversible step. Continue reading