Progress and History

by Unknown

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 class 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 fashioned, 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 pass 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 illustrations 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 passes from air into water or from air into glass. 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 illustrates 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 passed 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 incumbent 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 assistance 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.