Science and the modern world

by Alfred North Whitehead

In this century the notion of the mechanical explanation of all the processes of nature finally hardened into a dogma of science. The notion won through on its merits by reason of an almost miraculous series of triumphs achieved by the mathematical physicists, culminating in the Méchanique Analytique of Lagrange, which was published in 1787. Newton’s Principia was published in 1687, so that exactly one hundred years separates the two great books. This century contains the first period of mathematical physics of the modern type. The publication of Clerk Maxwell’s Electricity and Magnetism in 1873 marks the close of the second period. Each of these three books introduces new horizons of thought affecting everything which comes after them.

In considering the various topics to which mankind has bent its systematic thought, it is impossible not to be struck with the unequal distribution of ability among the different fields. In almost all subjects there are a few outstanding names. For it requires genius to create a subject as a distinct topic for thought. But in the case of many topics, after a good beginning very relevant to its immediate occasion, the subsequent development appears as a weak series of flounderings, so that the whole subject gradually loses its grip on the evolution of thought. It was far otherwise with mathematical physics. The more you study this subject, the more you will find yourself astonished by the almost incredible triumphs of intellect which it exhibits. The great mathematical physicists of the eighteenth and first few years of the nineteenth century, most of them French, are a case in point: Maupertuis, Clairaut, D’Alembert, Lagrange, Laplace, Fourier, form a series of names, such that each recalls to mind some achievement of the first rank. When Carlyle, as the mouthpiece of the subsequent Romantic Age, scoffingly terms the period the Age of Victorious Analysis, and mocks at Maupertuis as a ‘sublimish gentleman in a white periwig,’ he only exhibits the narrow side of the Romanticists whom he is then voicing.

It is impossible to explain intelligently, in a short time and without technicalities, the details of the progress made by this school. I will, however, endeavour to explain the main point of a joint achievement of Maupertuis and Lagrange. Their results, in conjunction with some subsequent mathematical methods due to two great German mathematicians of the first half of the nineteenth century, Gauss and Riemann, have recently proved themselves to be the preparatory work necessary for the new ideas which Herz and Einstein have introduced into mathematical physics. Also they inspired some of the best ideas in Clerk Maxwell’s treatise, already mentioned in this lecture.

They aimed at discovering something more fundamental and more general than Newton’s laws of motion which were discussed in the previous lecture. They wanted to find some wider ideas, and in the case of Lagrange some more general means of mathematical exposition. It was an ambitious enterprise, and they were completely successful. Maupertuis lived in the first half of the eighteenth century, and Lagrange’s active life lay in its second half. We find in Maupertuis a tinge of the theologic age which preceded his birth. He started with the idea that the whole path of a material particle between any limits of time must achieve some perfection worthy of the providence of God. There are two points of interest in this motive principle. In the first place, it illustrates the thesis which I was urging in my first lecture that the way in which the medieval church had impressed on Europe the notion of the detailed providence of a rational personal God was one of the factors by which the trust in the order of nature had been generated. In the second place, though we are now all convinced that such modes of thought are of no direct use in detailed scientific enquiry, Maupertuis’ success in this particular case shows that almost any idea which jogs you out of your current abstractions may be better than nothing. In the present case what the idea in question did for Maupertuis was to lead him to enquire what general property of the path as a whole could be deduced from Newton’s laws of motion. Undoubtedly this was a very sensible procedure whatever one’s theological notions. Also his general idea led him to conceive that the property found would be a quantitative sum, such that any slight deviation from the path would increase it. In this supposition he was generalising Newton’s first law of motion. For an isolated particle takes the shortest route with uniform velocity. So Maupertuis conjectured that a particle travelling through a field of force would realise the least possible amount of some quantity. He discovered such a quantity and called it the integral action between the time limits considered. In modern phraseology it is the sum through successive small lapses of time of the difference between the kinetic and potential energies of the particle at each successive instant. This action, therefore, has to do with the interchange between the energy arising from motion and the energy arising from position. Maupertuis had discovered the famous theorem of least action. Maupertuis was not quite of the first rank in comparison with such a man as Lagrange. In his hands and in those of his immediate successors, his principle did not assume any dominating importance. Lagrange put the same question on a wider basis so as to make its answer relevant to actual procedure in the development of dynamics. His Principle of Virtual Work as applied to systems in motion is in effect Maupertuis’ principle conceived as applying at each instant of the path of the system. But Lagrange saw further than Maupertuis. He grasped that he had gained a method of stating dynamical truths in a way which is perfectly indifferent to the particular methods of measurement employed in fixing the positions of the various parts of the system. Accordingly, he went on to deduce equations of motion which are equally applicable whatever quantitative measurements have been made, provided that they are adequate to fix positions. The beauty and almost divine simplicity of these equations is such that these formulae are worthy to rank with those mysterious symbols which in ancient times were held directly to indicate the Supreme Reason at the base of all things. Later Herz—inventor of electromagnetic waves—based mechanics on the idea of every particle traversing the shortest path open to it under the circumstances constraining its motion; and finally Einstein, by the use of the geometrical theories of Gauss and Riemann, showed that these circumstances could be construed as being inherent in the character of space-time itself. Such, in barest outline, is the story of dynamics from Galileo to Einstein.

Meanwhile Galvani and Volta lived and made their electric discoveries; and the biological sciences slowly gathered their material, but still waited for dominating ideas. Psychology, also, was beginning to disengage itself from its dependence on general philosophy. This independent growth of psychology was the ultimate result of its invocation by John Locke as a critic of metaphysical licence. All the sciences dealing with life were still in an elementary observational stage, in which classification and direct description were dominant. So far the scheme of abstractions was adequate to the occasion.

In the realm of practice, the age which produced enlightened rulers, such as the Emperor Joseph of the House of Hapsburg, Frederick the Great, Walpole, the great Lord Chatham, George Washington, cannot be said to have failed. Especially when to these rulers, it adds the invention of parliamentary cabinet government in England, of federal presidential government in the United States, and of the humanitarian principles of the French Revolution. Also in technology it produced the steam-engine, and thereby ushered in a new era of civilisation. Undoubtedly, as a practical age the eighteenth century was a success. If you had asked one of the wisest and most typical of its ancestors, who just saw its commencement, I mean John Locke, what he expected from it, he would hardly have pitched his hopes higher than its actual achievements.

In developing a criticism of the scientific scheme of the eighteenth century, I must first give my main reason for ignoring nineteenth century idealism—I am speaking of the philosophic idealism which finds the ultimate meaning of reality in mentality that is fully cognitive. This idealistic school, as hitherto developed, has been too much divorced from the scientific outlook. It has swallowed the scientific scheme in its entirety as being the only rendering of the facts of nature, and has then explained it as being an idea in the ultimate mentality. In the case of absolute idealism, the world of nature is just one of the ideas, somehow differentiating the unity of the Absolute: in the case of pluralistic idealism involving monadic mentalities, this world is the greatest common measure of the various ideas which differentiate the various mental unities of the various monads. But, however you take it, these idealistic schools have conspicuously failed to connect, in any organic fashion, the fact of nature with their idealistic philosophies. So far as concerns what will be said in these lectures, your ultimate outlook may be realistic or idealistic. My point is that a further stage of provisional realism is required in which the scientific scheme is recast, and founded upon the ultimate concept of organism.

In outline, my procedure is to start from the analysis of the status of space and of time, or in modern phraseology, the status of space-time. There are two characters of either. Things are separated by space, and are separated by time: but they are also together in space, and together in time, even if they be not contemporaneous. I will call these characters the ‘separative’ and the ‘prehensive’ characters of space-time. There is yet a third character of space-time. Everything which is in space receives a definite limitation of some sort, so that in a sense it has just that shape which it does have and no other, also in some sense it is just in this place and in no other. Analogously for time, a thing endures during a certain period, and through no other period. I will call this the ‘modal’ character of space-time. It is evident that the modal character taken by itself gives rise to the idea of simple location. But it must be conjoined with the separative and prehensive characters.

For simplicity of thought, I will first speak of space only, and will afterwards extend the same treatment to time.

The volume is the most concrete element of space. But the separative character of space, analyses a volume into sub-volumes, and so on indefinitely. Accordingly, taking the separative character in isolation, we should infer that a volume is a mere multiplicity of non-voluminous elements, of points in fact. But it is the unity of volume which is the ultimate fact of experience, for example, the voluminous space of this hall. This hall as a mere multiplicity of points is a construction of the logical imagination.