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ancient civilisation, we find a complete change. The axiom of the uniformity and knowableness of natural events stands removed above all doubt; the effort after this knowledge has found its destined path. Positive natural science, directed to the precise investigation of particular facts, and the clear co-ordination of the results of these inquiries, has already completely separated itself from the speculative philosophy of nature, which seeks to reach beyond the bounds of experience, and rise to the ultimate causes of things.

Physical research has attained a definite method. Deliberate has supplanted merely casual observation: instruments lend precision to observation and secure its results; experiments even are being made.

The exact sciences, by a brilliant elaboration and perfecting of mathematics, had secured that instrument which, in the hands of the Greeks, the Arabs, and the Teutono-Romanic peoples of modern times, step by step brought about the most magnificent practical and theoretical results. Plato and Pythagoras inspired their pupils to the cultivation of a mathematical sense.

The books of Euklid constitute still in the country of Newton, after more than two thousand years, the foundation of mathematical instruction, and the primitive synthetic method celebrated in the Mathematical Elements of Natural Philosophy-(Naturalis philosophiae principia mathematica)-its last and greatest triumph.

Astronomy, under the guidance of subtle and complicated hypotheses as to the motion of the heavenly bodies, accomplished incomparably more than those primitive diviners of the stars, the peoples of India, Babylon, and Egypt, had ever succeeded in attaining. A very nearly exact calculation of the positions of the planets, of eclipses of the sun and moon, an accurate representation and grouping of the fixed stars, does not exhaust the list of what was achieved; and even the root-idea of the Copernican system, the placing of the sun in the centre of the

universe, is to be found in Aristarchos of Samos, with whose views Copernicus was very probably acquainted.

If we inspect the map of Ptolemy, we find still, it is true, the fabulous southern land uniting Africa to Further India, and converting the Indian Ocean into a second. and greater Mediterranean; but Ptolemy represents this country as purely hypothetical; and how charming it looks already in Europe and the inner portions of Asia and Africa! Long before the spherical shape of the earth had been generally recognised. A methodical indication of place by means of degrees of longitude and latitude forms a strong support for the maintenance of what has been reached, and the incorporation of all fresh discoveries. Even the circumference of the earth had been already estimated by means of an ingenious astronomical method. Though this estimate contained an error, yet this very error led to the discovery of America, when Columbus, relying upon Ptolemy, sought the western passage to the East Indies.

Long before Ptolemy the researches of Aristotle and his predecessors had diffused a mass of information on the fauna and flora of more or less distant countries. Accurate description, anatomical examination of the internal structure of organic bodies, paved the way for a comprehensive survey of the forms which, from the lowest upward to the highest, were conceived as a progressive realisation of formative forces, which end by producing in man the most perfect of earthly things. Although in this view again numerous errors were involved, yet so long as the spirit of inquiry remained active, the foundation was of infinite value. The victorious campaigns of Alexander in the East enriched the sciences, and by the help of comparison still further enlarged and opened the field of observation. The industry of Alexandria accumulated and sifted materials. And so, when the elder Pliny attempted in his encyclopedic work to represent the whole field of nature and art, a nearer insight into the relations between

human life and the universe was already possible. To this restless spirit, who closed his great work with an invocation to Nature, the universal mother, and ended his life whilst engaged in observing a volcano, the influence of nature upon the intellectual life of mankind constituted a fruitful point of view, and an inspiring stimulus to inquiry. The physics of the ancients embrace a notion, built upon experiment, of the main principles of acoustics, of optics, of statics, and the theory of gases and vapours. From the researches of the Pythagoreans into the pitch and depth of musical tones, as conditioned by the relative masses of the sounding bodies, to the experiments of Ptolemy on the refraction of light, the spirit of Hellenic research accomplished a long career of fruitful productiveness. The mighty buildings, war-engines, and earthworks of the Romans were based upon a scientific theory, by the exact application of which they were carried out with the utmost possible care and expedition, while the much more colossal works of the Oriental nations were produced rather by the prodigal expenditure of time and labour under the coercion of despotic dynasties.

Scientific medicine, culminating in Galen of Pergamos, had already explained the bodily life in its most difficult element-the nervous activity. The brain, previously regarded as an inert mass, whose use was still less understood than that of the spleen in modern times, had been elevated to the seat of the soul and the functions of sensation. Sömmering, in the last century, found the theory of the brain almost where Galen had left it. The ancients were acquainted with the importance of the spinal marrow, and thousands of years before Sir Charles Bell they had distinguished the nerves of sensibility and movement; and Galen cured paralysis of the fingers, to the astonishment of his contemporaries, by acting upon those parts of the spine from which the implicated nerves took their rise. No wonder, then, that Galen already regarded ideas as results of bodily conditions.

When we behold knowledge thus accumulating from all sides-knowledge which strikes deep into the heart of nature, and already presupposes the axiom of the uniformity of events-we must ask the question, How far did ancient Materialism contribute to the attainment of this knowledge and these views?

And the answer to this question will at first sight appear very curious. For not only does scarcely a single one of the great discoverers-with the solitary exception of Demokritos-distinctly belong to the Materialistic school, but we find amongst the most honourable names a long series of men belonging to an utterly opposite, idealistic, formalistic, and even enthusiastic tendency.

And special notice must here be paid to mathematics. Plato, the first father of an enthusiasm which became in the course of history at one time beautiful and profound, at another fanatical and delirious, is at the same time the intellectual progenitor of a line of inquirers who carried the clearest and most consequent of all sciences, mathematics, to the highest point it was to reach in antiquity. The Alexandrian mathematicians belonged almost wholly to the Platonic school, and even when the development of Neo-Platonism began, and the troubled fermentations of the great religious crisis made their way into philosophy, this school still produced great mathematicians. Theon and his noble daughter Hypatia, martyred by the Christian rabble, may serve to indicate this stage. A similar tendency proceeded from Pythagoras, whose school produced in Archytas a mathematician of the first order. By the side of these the Epikurean Polyaenos is scarcely to be mentioned. Even Aristarchos of Samos, the forerunner of Copernicus, clung to Pythagorean traditions. The great Hipparchos, the discoverer of the precession of the equinoxes, believed in the divine origin of the human soul. Eratosthenes belongs to the middle academy, which corrupted Platonism by a sceptical element. Pliny, Ptolemy, Galen, without any exact system, leaned to pantheistic

views, and would perhaps, two hundred years earlier, have been confounded with the proper followers of Materialism under the common name of Atheism and Naturalism. But Pliny favoured no philosophical system, although he stands in open opposition to popular beliefs, and leans in his views to Stoicism. Ptolemy was entangled in astrology, and in the general principles of his philosophy, at all events, follows Aristotle rather than Epikuros. Galen, who was more of a philosopher than any of them, is an Eclectic, and is acquainted with the most various systems, yet he shows himself least inclined to the Epikurean: only in the theory of knowledge he held the immediate certainty of sense-perceptions; but he supplemented it by assuming immediate truths of the reason, which are certain previous to all experience.60

We see easily enough, however, that this slender participation of Materialisin in the achievements of positive inquiry is not casual; that it is especially not to be attributed merely to the quietistic and contemplative character of Epikureanism, but that, in fact, the ideal element (Moment) with the conquerors of the sciences stands in the closest connection with their inventions and discoveries.

Here we must not allow an appreciation to escape us of the great truth that it is not what is objectively right and reasonable that most furthers us, not even that which

60 The passage contained at p. 65 of the first edition, in which the Index of Humboldt's "Kosmos" was employed to prove the scientific importance of Aristotle, has been retracted on considering that the preservation of the Aristotelian writings in the general destruction of the Greek literature was sufficiently decisive on this point. It is therefore perhaps to be doubted whether the influence of Aristotle has not been too favourably estimated in the passage of Humboldt: "In Plato's hoher Achtung für mathematische Gedankenentwicklung, wie in den alle Organismen umfassenden

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