The period from the end of the seventeenth and beginning of the eighteenth centuries saw a complete transformation of the world of science rooted in the conquests of the previous period. In England, the victory of the bourgeoisie in the Civil War, and the subsequent compromise of a constitutional monarchy after 1688, provided relatively freer conditions for the development of scientific research and investigation. At the same time, the growth of trade and, increasingly, manufacture, created a need for more advanced technology and the capital necessary to pay for it. It was a period of unprecedented innovation and scientific advance.
Improvements in optics made possible the invention of the microscope. In France, Gassendi resurrected the atomic theories of Democritus and Epicurus. In Germany, Von Guericke invented the air-pump. Robert Boyle made significant progress in chemistry. The discoveries of Copernicus, Tycho Brache, Kepler, Galileo and Huygens prepared the ground for Newton’s revolution in astronomy, which were made necessary by the demand for more accurate navigation. The predominant method of science at the time was mechanistic: that is, that natural phenomena were to be interpreted in terms of form, size, position, arrangement, and motion of corpuscles, and their behaviour was to be explained exclusively in terms of contact with other particles.
The chief exponent of the new science was Sir Isaac Newton (1643-1727). Newton, who became President of the Royal Society in 1703, exercised a colossal influence, not just in science, but in philosophy and the general mode of thinking of the period in which he lived and later. The poet Alexander Pope sums up the adulatory attitude of contemporary Englishmen with his verse:
"Nature and Nature’s laws lay hid in night:
God said ‘Let Newton be!’ and all was light."
Newton was born on Christmas day 1642, the year when Galileo died and the Civil War broke out between Charles I and Parliament. In 1687, he published his famous Principia Mathematica, which set forth three laws of motion—the law of inertia, law of proportionality of force and velocity, law of equality of action and counteraction, from which the basic principles of classical physics and mechanics were deduced. Here he set out and proved his theory of universal gravitation. This marks the definitive break with the old Aristotelean-Ptolomaic world-picture. Instead of celestial spheres operated by angels, Newton put forward a scheme of a universe functioning according to the laws of mechanics without the need for any divine intervention whatsoever, except for an initial impulse needed to set the whole thing in motion.
A typical product of the English empirical school, Newton was not much bothered about this, preferring to ask no questions about the role of the Almighty in his mechanical universe. For their part, the religious Establishment, personified by Bishop Sprat, bowing to the inevitable, advocated a compromise with science, much like the compromise between King William and Parliament, which held in place for about a century, until it was overthrown by Darwin’s discoveries. The demands of capitalism ensured that science was left in peace to get on with the job.
Like the great thinkers of the Renaissance, the scientists of Newton’s age were mostly men with a broad vision of science. Newton himself was not only an astronomer, but also a mathematician, optician and mechanic, and even a chemist. His contemporary and friend, Robert Hook, was not only the greatest experimental physicist before Faraday, but was also a chemist, mathematician, biologist and inventor, who shares with Papin the credit of preparing the way to the steam engine.
Invention of Calculus
The discovery of the infinitesimal calculus, which revolutionised mathematics, has been variously ascribed to Newton and Leibniz. It is possible that both came to the same conclusion independently. In his Method of Fluxions, Newton sets out from the conception of a line as a "flowing quantity" (the "fluent"), and the velocity by which the line "flows" is described as its fluxion. Newton refers to a "moment" as an infinitely small length by which the fluent increased in an infinitely small time. This represented a complete break with the traditional method of mathematics, which totally excluded the concept of infinity and infinitesimals, which were not supposed to exist. The colossal advantage of this method was that it allowed mathematics for the first time to deal with motion. Indeed, Newton refers to it as the "mathematics of motion and growth." It was this instrument that permitted him to formulate the laws of planetary motion discovered by Kepler as general laws of motion and matter.
The discovery of the infinitesimal calculus was fundamental for the whole development of science. Yet it involves a contradiction which immediately caused a controversy, which lasted a long time. The first detractor of calculus was none other than Bishop Berkeley, who objected to the use of infinitesimally small quantities. This, he argued, was in contradiction to logic, and therefore unacceptable. "What are these fluxions?" he asked. "The velocities of evanescent increments. And what are these same evanescent increments? They are neither finite quantities, nor quantities infinitely small, nor yet nothing. May we not call them the ghosts of departed quantities?" (Quoted by Hooper, op. cit., p. 322.)
Here again, we see the fundamental limitation of the method of formal logic. Its basic premise is the elimination of contradiction. Yet motion is a contradiction—that of being and not being in the same place at the same time. In the first volume of his Science of Logic, Hegel deals in detail with the differential and integral calculus, and shows that it deals with magnitudes that are in the process of disappearing, neither before, when they are finite magnitudes, nor after, when they are nothing, but in a state which is and is not. This is in clear contradiction to the laws of formal logic, and hence provoked the indignant assaults of orthodox mathematicians and logicians. Despite all objections, the new mathematics achieved brilliant results in solving problems which could not be solved by the traditional methods. Yet when Newton published his Principia, he felt obliged to recast it in the form of classical Greek geometry, so as to cover up the fact that he had used the new method in all his calculations.
Newton also advanced the theory that light was composed of particles, tiny corpuscles projected through space by luminous bodies. In the early 19th century, this theory was abandoned in favour of Huygen’s wave theory, which was linked to the idea of the "ether," a hypothetical weightless, invisible medium, which, rather like the "dark matter" of modern astronomers, could not be detected by our senses, but which supposedly permeated space and filled the gaps between the air and other matter.
This theory seemed to explain all the known phenomena of light until 1900, when Max Planck put forward the idea that light was transmitted in small packets of energy or "quanta." Thus, the old Newtonian particle theory was revived, but with a striking difference. It was discovered that sub atomic particles behave both like waves and particles. Such a contradictory and "illogical" concept shocked the formal logicians as much as the differential and integral calculus had done. Eventually, they were compelled reluctantly to accept it, purely because, as with the calculus, the theory was backed up by practical results. But at every decisive turn, we see the same clash between the real advances of science and the obstacles placed in its way by outmoded ways of thinking.
The revolutionary contribution of Newton to science is not in doubt. Yet his legacy was not an unmixed blessing. The uncritical adulation which he received in his lifetime in England obscured the important role of his contemporaries, like Hooke, who anticipated his Principia by seven years, though without the necessary mathematical backing, and Leibniz, the German philosopher who was probably the real discoverer of the calculus. Several of his most important theories were in fact put forward much earlier by Galileo and Kepler. His major role was to systematise and sum up the discoveries of the past period, and give them a general form, backed up by mathematical calculations.
On the negative side, Newton’s enormous authority gave rise to a new orthodoxy that was to inhibit scientific thinking for a long time. "His abilities were so great," writes Bernal, "his, system so perfect, that they positively discouraged scientific advance for the next century, or allowed it only in the regions he had not touched." (Bernal, op. cit., p. 343.) The limitations of the English school of empiricism was summed up in his celebrated phrase: hypothesis non fingo—I make no hypotheses. This slogan became the battle cry of empiricism, yet bore absolutely no relation to the actual method of science, including that of Newton, who, for example, in the field of optics, made "numerous conjectures as to the physical causes of optical and other phenomena and even partly propounding them as facts. Thus, in his explanation of what were afterwards called Newton’s rings, he treated the alternate fits of easy transmission and easy reflection along a ray of light as experimentally established facts, which he then made use of." (Forbes and Dijksterhaus, op. cit., Vol. 1, p. 247.)
The advances of science were enormous. Yet the general world-view bequeathed by the period was conservative. The static and mechanical outlook coloured mens’ minds for generations, as Engels points out:
"But what especially characterises this period is the elaboration of a peculiar general outlook, the central point of which is the view of the absolute immutability of nature. In whatever way nature itself might have come into being, once present it remained as it was as long as it continued to exist. The planets and their satellites, once set in motion by the mysterious ‘first impulse,’ circled on and on in their predestined ellipses for all eternity, or at any rate until the end of all things. The stars remained for ever fixed and immovable in their places, keeping one another therein by ‘universal gravitation.’ The earth had remained the same without alteration from all eternity or, alternatively, from the first day of its creation. The ‘five continents’ of the present day had always existed, and they had always had the same mountains, valleys, and rivers, the same climate, and the same flora and fauna, except in so far as change or transplantation had taken place at the hand of man. The species of plants and animals had been established once for all when they came into existence; like continually produced like, and it was already a good deal for Linnaeus to have conceded that possibly here and there new species could have arisen by crossing. In contrast to the history of mankind, which develops in time, there was ascribed to the history of nature only an unfolding in space. All change, all development in nature, was denied. Natural science, so revolutionary at the outset, suddenly found itself confronted by an out-and-out conservative nature, in which even today everything was as it had been from the beginning and in which—to the end of the world or for all eternity—everything would remain as it had been since the beginning." (Engels, The Dialectics of Nature, p. 34.)
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