The Day the Universe Changed - James Burke [74]
Descartes’ universe was a cold, empty, mechanical place. But the story of how he made a major contribution to the mathematical explanation of its operation strikes a more personal note. One day in Mersenne’s cell, during one of their twice-weekly meetings, Descartes noticed a fly buzzing round. It occurred to him that the position of the fly in space was always at a point which could be intersected by two lines, one coming from the side, one from below, crossing at right angles over the fly. These axes would provide co-ordinate axes for the fly’s position at any time, and could be scaled against a fixed pair of lines set to one side and at right angles to each other. This new system for exact coordination is what we today call a graph.
The graph did away with the need for Kepler’s cumbersome geometrical drawings. Its importance in the history of science cannot be overestimated. It permitted any series of positions along any line to be described in terms of its co-ordinates. Any trajectory could be described by its y (vertical scale) and x (horizontal scale) values, which would alter according to its movement in either axis. A trajectory rising at 45 degrees, for instance, would always have equal y and x values and so could be described as a ‘y = x’ line.
The new analytical geometry permitted all forms of motion to be analysed theoretically. The equations for the curve of any trajectory could be written and then manipulated mathematically to show what would happen to the projectile under altered conditions such as increase in propulsion or weight. Of course this ability was of particular use in the study of planetary orbits, where the projectiles were out of reach. Now the principal need was to be able to make more precise measurements of the data to be so manipulated.
Examples of how Descartes’ graph worked. Left, the line in which ally andx values are equal can be described asy = x. Centre, the line represented by the equation y = 2x (for every horizontal unit of distance moved, the vertical distance is double). Right, a cannon-ball trajectory. The modern ballistic equation contains all factors involved (gravity, charge, weight of ball, and so on). A gun can thus be tested on paper.
By the middle of the seventeenth century such developments were already well under way. In 1628 William Harvey demonstrated the circulation of the blood. Jan Baptista van Helmont discovered the existence of gases some time before 1644. In 1646 Evangelista Torricelli produced a vacuum, as a result of which barometric pressure was able to be accurately measured by 1648. Otto von Guericke developed the vacuum pump. In England Robert Hooke and Robert Boyle examined the compressibility, elasticity and weight of air and showed it to be vital for respiration. In 1661 Boyle led the way to modern chemistry when he dispensed with the Aristotelian theory that all substances were made up of the four elements.
The rate of change was equally rapid in the development of scientific instruments, particularly precision instruments. By the last quarter of the century there were telescopes, pendulum clocks, screw micrometers, air and vacuum pumps, barometers and chronometers, bubble levels and, above all, microscopes. From 1660 on the microscope seemed to underline the mechanical nature of the universe as it revealed more and more minute forms of life and inorganic structures which evidently operated on mechanical principles. Experimental science was immensely stimulated by these advances.
In mid-century scientific societies were established all over Europe. The English Royal Society, founded in 1660 and given its royal charter in 1662, admitted not only experimenters but merchants and navigators too. The purpose of the society was to investigate nature and to find new ways of making the industries of England more efficient and profitable. In France, on the other hand, the Royal Academy of Sciences set up by Jean Baptiste Colbert, chief minister of Louis XIV, had purely industrial aims. The theories of Descartes were not allowed to be discussed.