Part 14 (1/2)
Before entering on a historical sketch of the most perfect example of human progress, it is of the first importance to realize its social foundation. This is the key-note, and it connects science throughout with the other aspects of our subject. Knowledge depends upon the free intercourse of mind with mind, and man advances with the increase and better direction of his knowledge. But when we consider the implications of any generalization which we can call 'a law of nature' the social co-operation involved becomes still more apparent. Geometry and astronomy--the measurement of the earth and the measurement of the heavens--dispute the honour of the first place in the historical order.
Both, of course, involved the still more fundamental conception of number and the acceptance of some unit for measurement. Now in each case and at every step a long previous elaboration is implied of intellectual conventions and agreements--conscious and unconscious--between many minds stretching back to the beginnings of conscious life: the simplest element of thought involves the co-operation of individual minds in a common product. Language is such a common product of social life and it prepares the ground for science. But science, as the exact formulation of general truths, attains a higher degree of social value, because it rises above the idioms of person or race and is universally acceptable in form and essence. Such is the intrinsic nature of the process, and the historical circ.u.mstances of its beginnings make it clear. It was the quick mind of the Greek which acted as the spark to fire the trains of thought and observation which had been acc.u.mulating for ages through the agency of the priests in Egypt and Babylonia. The Greeks lived and travelled between the two centres, and their earliest sages and philosophers were men of the most varied intercourse and occupation. Their genius was fed by a wide sympathy and an all-embracing curiosity. No other people could have demonstrated so well the social nature of science from its inception, and they were planting in a soil well prepared. In Egypt conspicuously and in Chaldea also to a less extent there had been a social order which before the convulsions of the last millennium B.C. had lasted substantially unchanged for scores of centuries. This order was based upon a religious discipline which connected the sovereigns on earth with the divine power ruling men from the sky. Hence the supreme importance of the priesthood and their study of the movements of the heavenly bodies. The calendar, which they were the first to frame, was thus not only or even primarily a work of practical utility but of religious meaning and obligation. The priests had to fix in advance the feast days of G.o.ds and kings by astronomical prediction. Their standards and their means of measurement were rough approximations. Thus the 360 degrees into which the Babylonians taught us to divide the circle are thought to have been the nearest round number to the days of the year. The same men were also capable of the more accurate discovery that the side of a hexagon inscribed in a circle was equal to the radius and gave us our division of sixty minutes and sixty seconds with all its advantages for calculation. In Egypt, if the surveyors were unaware of the true relation between a triangle and the rectangle on the same base, they had yet established the carpenter's rule of 3, 4 and 5 for the sides of a right-angled triangle.
How much the Greeks drew from the ancient priesthoods we shall never know, nor how far the priests had advanced in those theories of general relations which we call scientific. But one or two general conclusions as to this initial stage of scientific preparation may well be drawn.
One is that a certain degree of settlement and civilization was necessary for the birth of science. This we find in these great theocracies, where sufficient wealth enabled a cla.s.s of leisured and honoured men to devote themselves to joint labour in observing nature and recording their observations. Another point is clear, namely, that the results of these early observations, crude as they were, contributed powerfully to give stability to the societies in which they arose. The younger Pliny points out later the calming effect of Greek astronomy on the minds of the Eastern peoples, and we are bound to carry back the same idea into the ancient settled communities where astronomy began and where so remarkable an order prevailed for so long during its preparation.
But however great the value we allow to the observations of the priests, it is to the Ionian Greeks that we owe the definite foundation of science in the proper sense; it was they who gave the raw material the needed accuracy and generality of application, A comparison of the societies in the nearer East to which we have referred, with the history of China affords the strongest presumption of this. In the later millenniums B.C. the Chinese were in many points ahead of the Babylonians and Egyptians. They had made earlier predictions of eclipses and more accurate observations of the distance of the sun from the zenith at various places. They had, too, seen the advantages of a decimal system both in weights and measures and in the calculations of time. But no Greek genius came to build the house with the bricks that they had fas.h.i.+oned, and in spite of the achievements of the Chinese they remained until our own day the type in the world of a settled and contented, although unprogressive, conservatism.
Science then among its other qualities contains a force of social movement, and our age of rapid transformation has begun to do fuller justice to the work of the Greeks, the greatest source of intellectual life and change in the world. We are now fully conscious of the defects in their methods, the guesses which pa.s.s for observations, the metaphysical notions which often take the place of experimental results.[80] But having witnessed the latest strides in the unification of science on mathematical lines, we are more and more inclined to prize the geometry and astronomy of the Greeks, who gave us the first constructions on which the modern mechanical theories of the universe are based. We shall quote from them here only sufficient ill.u.s.trations to explain and justify this statement.
The first shall be what is called Euclidean geometry, but which is in the main the work of the Pythagorean school of thinkers and social reformers who flourished from the seventh to the fifth centuries B.C.
This formed the greater part of the geometrical truth known to mankind until Descartes and the mathematicians recommenced the work in the seventeenth century. The second greatest contribution of the Greeks was the statics and the conics of which Archimedes was the chief creator in the third century B.C. In his work he gave the first sketch of an infinitesimal calculus and in his own way performed an integration. The third invaluable construction was the trigonometry by which Hipparchus for the first time made a scientific astronomy possible. The fourth, the optics of Ptolemy based on much true observation and containing an approximation to the general law.
These are a few outstanding landmarks, peaks in the highlands of Greek science, and nothing has been said of their zoology or medicine. In all these cases it will be seen that the advance consisted in bringing varying instances under the same rule, in seeing unity in difference, in discovering the true link which held together the various elements in the complex of phenomena. That the Greek mind was apt in doing this is cognate to their idealizing turn in art. In their statues they show us the universal elements in human beauty; in their science, the true relations that are common to all triangles and all cones.
Ptolemy's work in optics is a good example of the scientific mind at work.[81] The problem is the general relation which holds between the angles of incidence and of refraction when a ray pa.s.ses from air into water or from air into gla.s.s. He groups a series of the angles with a close approximation to the truth, but just misses the perception which would have turned his excellent raw material into the finished product of science. His brick does not quite fit its place in the building. His formula _i_ (the angle of incidence) = _nr_ (the angle of refraction) only fits the case of very small angles for which the sine is negligible, though it had the deceptive advantage of including reflexion as one case of refraction. He did not pursue the argument and make his form completely general. Sin _i_ = _n_ sin _r_ escaped him, though he had all the trigonometry of Hipparchus behind him, and it was left for Snell and Descartes to take the simple but crucial step at the beginning of the seventeenth century.
The case is interesting for more than one reason. It shows us what is a general form, or law of nature in mathematical shape, and it also ill.u.s.trates the progress of science as it advances from the most abstract conceptions of number and geometry, to more concrete phenomena such as physics. The formula for refraction which Ptolemy helped to shape, is geometrical in form. With him, as with the discoverer of the right angle in a semicircle, the mind was working to find a general ideal statement under which all similar occurrences might be grouped.
Observation, the collection of similar instances, measurement, are all involved, and the general statement, law or form, when arrived at, is found to link up other general truths and is then used as a starting-point in dealing with similar cases in future. Progress in science consists in extending this mental process to an ever-increasing area of human experience. We shall see, as we go on, how in the concrete sciences the growing complexity and change of detail make such generalizations more and more difficult. The laws of pure geometry seem to have more inherent necessity and the observations on which they were originally founded have pa.s.sed into the very texture of our minds. But the work of building up, or, perhaps better, of organizing our experience remains fundamentally the same. Man is throughout both perceiving and making that structure of truth which is the framework of progress.
Ptolemy's work brings us to the edge of the great break which occurred in the growth of science between the Greek and the modern world. In the interval, the period known as the Middle Ages, the leading minds in the leading section of the human race were engaged in another part of the great task of human improvement. For them the most inc.u.mbent task was that of developing the spiritual consciousness of men for which the Catholic Church provided an incomparable organization. But the interval was not entirely blank on the scientific side. Our system of arithmetical notation, including that invaluable item the cipher, took shape during the Middle Ages at the hands of the Arabs, who appear to have derived it in the main from India. Its value to science is an excellent object-lesson on the importance of the details of form. Had the Greeks possessed it, who can say how far they might have gone in their applications of mathematics?
Yet in spite of this drawback the most permanent contribution of the Greeks to science was in the very sphere of exact measurement where they would have received the most a.s.sistance from a better system of calculation had they possessed it. They founded and largely constructed both plane and spherical geometry on the lines which best suit our practical intelligence. They gave mankind the framework of astronomy by determining the relative positions of the heavenly bodies, and they perceived and correctly stated the elementary principles of equilibrium.
At all these points the immortal group of men who adopted the Copernican theory at the Renascence, began again where the Greeks had left off. But modern science starts with two capital improvements on the work of the Greeks. Measurement there had been from the first, and the effort to find the constant thing in the variable flux; and from the earliest days of the Ionian sages the scientific mind had been endeavouring to frame the simplest general hypothesis or form which would contain all the facts. But the moderns advanced decisively, in method, by experimenting and verifying their hypotheses, and in subject-matter, by applying their method to phenomena of movement, which may theoretically include all facts biological as well as physical. Galileo, the greatest founder of modern science, perfectly exemplifies both these new departures.
It is, perhaps, the most instructive and encouraging thing in the whole annals of progress to note how the men of the Renascence were able to pick up the threads of the Greeks and continue their work. The texture held good. Leonardo da Vinci, whose birth coincides with the invention of the printing-press, is the most perfect reproduction in modern times of the early Greek sophos, the man of universal interests and capacity.
He gave careful and admiring study to Archimedes, the greatest pure man of science among the Greeks, the one man among them whose works, including even his letters, have come down to us practically complete. A little later, at the beginning of the sixteenth century, Copernicus gained from the Pythagoreans the crude notion of the earth's movement round a great central fire, and from it he elaborated the theory which was to revolutionize thought. Another half-century later the works of Archimedes were translated into Latin and for the first time printed.
They thus became well known before the time of Galileo, who also carefully studied them. At the beginning of the seventeenth century Galileo made the capital discoveries which established both the Copernican theory and the science of dynamics. Galileo's death in 1642 coincides with the birth of Sir Isaac Newton.
Such is the sequence of the most influential names at the turning-point of modern thought.
Galileo's work, his experiments with falling bodies and the revelations of his telescope, carried the strategic lines of Greek science across the frontiers of a New World, and Newton laid down the lines of permanent occupation and organized the conquest. Organization, the formation of a network of lines connected as a whole, and giving access to different parts of the world of experience, is perhaps the best image of the growth of science in the mind of mankind. It will be seen that it does not imply any exhaustion of the field, nor any identification of all knowledge with exact or systematic knowledge. The process is rather one of gradual penetration, the linking up and extension of the area of knowledge by well-defined and connected methods of thought. No all-embracing plan thought out beforehand by the first founders of science, or any of their successors, can be applied systematically to the whole range of our experience. It has not been so in the past; still less does it seem possible in the future. For the most part the discoverer works on steadily in his own plot, occupying the nearest places first, and observing here and there that one of his lines runs into some one else's. Every now and then a greater and more comprehensive mind appears, able to treat several systems as one whole, to survey a larger area and extend that empire of the mind which, as Bacon tells us, is n.o.bler than any other.
Of such conquerors Newton was the greatest we have yet known, because he brought together into one system more and further-reaching lines of communication than any one else. He unified the forms of measurement which had previously been treated as the separate subjects of geometry, astronomy, and the newly-born science of dynamics. Celestial mechanics embraces all three, and is a fresh and decisive proof of the commanding influence of the heavenly bodies on human life and thought. Not by a horoscope, but by continued and systematic thought, humanity was unravelling its nature and destiny in the stars as well as in itself.
These are the two approaches to perfect knowledge which are converging more and more closely in our own time. Newton's work was the longest step yet taken on the mechanical side, and we must complete our notice of it by the briefest possible reference to the later workers on the same line, before turning to the sciences of life which began their more systematic evolution with the discovery of Harvey, a contemporary of Newton.
The seventeenth century, with Descartes' application of algebra to geometry, and Newton's and Leibnitz's invention of the differential and integral calculus, improved our methods of calculation to such a point that summary methods of vastly greater comprehensiveness and elasticity can be applied to any problem of which the elements can be measured. The mere improvement in the method of describing the same things (cf. e.g. a geometrical problem as written down by Archimedes with any modern treatise) was in itself a revolution. But the new calculus went much farther. It enabled us to represent, in symbols which may be dealt with arithmetically, any form of regular movement.
As movement is universal, and the most obvious external manifestation of life itself, the hopes of a mathematical treatment of all phenomena are indefinitely enlarged, for all fresh laws or forms might conceivably be expressed as differential equations. So to the vision of a Poincare the human power of prediction appears to have no a.s.signable theoretical limit.
The seventeenth century which witnessed this momentous extension of mathematical methods, also contains the cognate foundation of scientific physics. Accurate measurement began to be applied to the phenomena of light and heat, the expansion of gases, the various changes in the forms of matter apart from life. The eighteenth century which continued this work, is also and most notably marked by the establishment of a scientific chemistry. In this again we see a further extension of accurate measurement: another order of things different in quality began to be treated by a quant.i.tative a.n.a.lysis. Lavoisier's is the greatest name. He gave a clear and logical cla.s.sification of the chemical elements then known, which served as useful a purpose in that science, as cla.s.sificatory systems in botany and zoology have done in those cases. But the crucial step which established chemistry, a step also due to Lavoisier, was making the test of weight decisive. 'The balance was the _ultima ratio_ of his laboratory.' His first principle was that the total weight of all the products of a chemical process must be exactly equal to the total weight of the substances used. From this, and rightly disregarding the supposed weight of heat, he could proceed to the discovery of the accurate proportions of the elements in all the compounds he was able to a.n.a.lyse.
Since then the process of mathematical synthesis in science has been carried many stages further. The exponents of this aspect of scientific progress, of whom we may take the late M. Henri Poincare as the leading representative in our generation, are perfectly justified in treating this gradual mathematical unification of knowledge with pride and confidence. They have solid achievement on their side. It is through science of this kind that the idea of universal order has gained its sway in man's mind. The occasional attacks on scientific method, the talk one sometimes hears of 'breaking the fetters of Cartesian mechanics', seem to suggest that the great structure which Galileo, Newton, and Descartes founded is comparable to the false Aristotelianism which they destroyed. The suggestion is absurd: its chief excuse is the desire to defend the autonomy of the sciences of life, about which we have a word to say later on. But we must first complete our brief mention of the greatest stages on the mechanical side, of which a full and vivid account may be found in such a book as M. Poincare's _Science et Hypothese_.
Early in the nineteenth century a trio of discoverers, a Frenchman, a German, and an Englishman, established the theory of the conservation of energy. To the labours of Sadi Carnot, Mayer, and Joule is due our knowledge of the fact that heat which, as a supposed ent.i.ty, had disturbed the physics and chemistry of the earlier centuries, was itself another form of mechanical energy and could be measured like the rest.
Later in the century another capital step in synthesis was taken by the foundation of astrophysics, which rests on the ident.i.ty of the physics and chemistry of the heavenly bodies with those of the earth.
The known universe thus becomes still more one. Later researches again, especially those of Maxwell, tend to the identification of light and heat with electricity, and in the last stage matter as a whole seems to be swallowed up in motion. It is found that similar equations will express all kinds of motion; that all are really various forms of the motion of something which the mind postulates as the thing in motion; we have in each case to deal with wave-movements of different length. The broad change, therefore, which has taken place since the mechanics of Newton is the advance from the consideration of ma.s.ses to that of molecules of smaller and smaller size, and the truth of the former is not thereby invalidated. Newton, Descartes, Fresnel, Carnot, Joule, Mayer, Faraday, Helmholtz, Maxwell appear as one great succession of unifiers. All have been engaged in the same work of consolidating thought at the same time that they extended it. Their conceptions of force, ma.s.s, matter, ether, atom, molecule have provisional validity as the imagined objective substratum of our experience, and the fact that we a.n.a.lyse these conceptions still further and sometimes discard them, does not in any way invalidate the law or general form in which they have enabled us to sum up our experience and predict the future.