The development of the pythagorean doctrine

ah „U. \ a> € IN: GREEK TANKERS CHAPTER IV. THE. DEVELOPMENT OF THE PYTHAGOREAN DOCTRINE. 1. VOLTAIRE called the later Pythagorean astronomy, connected with the name of Philolaus, a “ Gallimathias,” and Sir George Cornewall Lewis indicts it as “wild and fanciful.” But the great French writer with his frequently over-hasty judgments and the Englishman with his excess of conscientiousness have fallen into the same mistake. It is true that the doctrine in question is a tissue of truth and invention, but ‘its features of truth were its vital and fundamental parts, whereas the fictitious portions were merely a superficial covering which was soon to dissolve like smoke-wreaths. But if we are to understand the motives which inspired the cosmology of Philolaus, we must pause a moment at the commonest phenomena of the heavens. Each day the sun runs his course from east to west. Simultancously he climbs higher up the sky to sink at the end of a few months from the height he has reached, The combination of his daily and annual movements has the effect of the windings of a screw or spiral—something like the shell of a snail—and like it, too, the intervals between the circles contract as the zenith is approached. This view was hardly likely to satisfy inquirers who had approached the question of celestial motion in the confident belief that it was “simple, steady, and regular.” It may be permissible to blame this belief as a prejudice; but though it was in part a preconceived opinion, yet the closer observation of facts tended VAUT vaut

CHAPTER IV. THE DEVELOPMENT OF THE PYTHAGOREAN DOCTRINE. called the later Pythagorean astronomy, I. VOLTAIRE Gallimathias," connected with the name of Philolaus, a and Sir George Cornewall Lewis indicts it as "wild and But the great French writer with his frequently fanciful." " with his excess over-hasty judgments and the Englishman It of conscientiousness have fallen into the same mistake. is true that the doctrine in question is a tissue of truth and invention, but its features of truth were its vital and fundamental parts, whereas the fictitious portions were merely a superficial covering which was soon to dissolve But if we are to understand the like smoke-wreaths. motives which inspired the cosmology of Philolaus, we must pause a moment at the commonest phenomena of the heavens. Each day the sun runs his course from east to west. Simultaneously he climbs higher up the sky to sink at the end of a few months from the height he has reached. The combination of his daily and annual movements has the effect of the windings of a screw or spiral something and like it, too, the intervals like the shell of a snail between the circles contract as the zenith is approached. This view was hardly likely to satisfy inquirers who had approached the question of celestial motion in the confident belief that it was simple, steady, and regular." It may be permissible to blame this belief as a but though it was in part a preconceived prejudice " ; opinion, yet the closer observation facts tended

THE SYSTEM OF PHILOLAUS. generally to confirm it. And even where such confirma was wanting, the belief was of excellent use as a tion principle of research, just like the kindred assumption of a teleological purpose in the structure of organisms. It was possible to get rid of the confusing irregularity. For a complex movement may be irregular while the partial movements that compose it are regular. What was needed was an act of mental separation. And the clue was found by separating the daily movement of the sun from its At this point our early philosophers annual movement. had a brilliant flash of inspiration. They conceived the daily movement of the sun and moon, and indeed of all the whole starry heaven, as not real at all, but merely apparent. Their supposition that the earth was moving from west to east enabled them to dispense with the assumption that the sun, moon, planets, and fixed stars were moving in an opposite direction. The question suggests itself here, Did these Pythagoreans recognize and teach the rota tion of the earth round its axis ? Our answer is They did not do that, but they did recognize and teach the existence of a movement which operated in a precisely similar manner. It was, so to say, the rotation round an earth-ball with a considerably enlarged its axis of : They represented the earth as circu twenty-four hours round a central point, the nature of which will presently occupy us. Here, how ever, the reader should familiarize himself with a simple circumference. lating feature in of this doctrine. A moment s reflection will show him that, for any given point in the earth s surface, and for its shifting relations with the sun, moon, and stars, it makes not the remotest difference whether the ball on which it is situated revolves on course facing its of a day, the same or describes a directions, starting-point in the same its circular which brings limit axis in course, it of time. the while back to We can hardly exaggerate the importance of this discovery. The revelation that there were apparent heavenly motions broke the barrier that obstructed the path to further pro gress. The central position of the earth and its immobility VOL, l

had both been given up, and the way was open for after an interval the Copernican doctrine which followed is hardly sufficiently the extraordinary brevity of which Nor need we be at all surprised that an recognized. of rotation was adopted instead equivalent for the theory we never actually see a For though the of theory. its axis, yet changes in its position on luminary turning Nothing, are matters of daily and hourly observation. more natural than that scientific imagina which had just succeeded by a mighty effort in itself from the delusions of sense, should have then, could be tion, freeing been content to replace the apparent immobility of the earth by a movement moulded on familiar models, and one unique in its kind and entirely without a not by parallel. to The centre round which the earth was now admitted move served equally as the centre of the rest of the luminaries, which round the earth. a month ; had formerly been supposed to revolve The moon accomplished its course once the sun once a year ; the five planets visible to the naked eye required various periods, which, with the exception of Mercury and Venus, were considerably of fixed stars, whose daily longer; finally, the firmament rotation had been recognized as apparent, was similarly of its own, though of equipped with a circular movement a order a very much slower conception which may either desire for conformity, but mere the to due been have which is far more probably to be ascribed to that change of position already observed and taken in account which The daily move or rather, according to this theory, of the we call the precession of the equinoxes. ment of the sun took place in a plane which was now recognized to incline towards the plane in which the annual movements in other of the sun, moon, and planets were situated earth ; words, the obliquity, whether of the equator or of the and the new conception ecliptic, had been recognized, was thus completely adequate to explain the changes of the seasons. We come now to the problem of the central point round

THE CENTRAL-FIRE. which the heavenly bodies were to move in concentric It was no ideal centre, but rather an actual circles. body, consisting of universal or central fire. of Philolaus call The enemies dreary and fantastic fiction," but those who try to throw themselves with temperate judgment into the modes of thought obtaining in the dawn of it "a science will rather call it "the product of analogical inferences, the force of which must have been well-nigh irresistible." The assumption that the heavenly bodies described circles was not merely approximately true, but apart from the circular segments traversed by the sun and moon on the firmament, it appeared that no other conclusion could be derived from the circular courses described before our eyes by the circumpolar fixed stars that never set and ; that movement, like the movement of the whole though firmament of fixed stars, had now been recognized as purely apparent yet the daily motion of the earth that took its place was bound to have the same circular character. Here, accord ingly, the type was given, conformably with which all the But human experience heavenly bodies had to move. supplies no example of circular movements without an actual centre. wheel turns on its axis a stone, attached to a string for the purpose of slinging, turns round the hand which holds it and which sets it in motion and, finally, when divine worship invited Greek men and women A ; ; to the dance, the altar of the god formed the centre of and rhythmic paces. It may be asked, how ever, what need there was of inventing a central fire, when it actually existed and was visible to every man s eye. What was wanted was a centre of motion and a source of vigour and life. But instead of accrediting the universal light of the sun with the rank that belonged to it, a lumi nous body was invented whose rays no mortal eye had their solemn seen, and, considering that the habitable side of the earth was turned away from the central fire, no mortal eye would ever see. It was an hypothesis removed by a perverse in genuity from every chance of verification, and one wonders why its mistaken authors did not rather jump straight away at the heliocentric doctrine, and rest satisfied therewith.

Three sufficiently valid solutions may be suggested for Remembering that the delusions of sense this problem. and that the human mind are only abandoned by degrees, least of resistance, we have first the path habitually follows was bound to be later heliocentric theory the that note to It was obviously than that of rotation round an axis. sun in a daily the round revolve earth impossible to let the have already we and and yearly course simultaneously, of the the Pythagorean to precedence learned justify A second consider rotation theory. equivalent over the able obstacle to the prompt admission of a heliocentric or we conceive, in the exact simi Copernican astronomy lay, moon. The great luminary of and sun the between larity sister of the night were visible day and his more modest men as two heavenly bodies regularly relieving each other and combining to measure time by their revolutions, and it was plainly impossible that, except by a process of elimination, shutting out every other issue, men would ever to be brought to believe that luminaries so closely connected differed in the fundamental point that the moon was con demned to ceaseless wandering while the sun was vowed to But, thirdly and chiefly, universal fire was satisfactory as the centre of the world than the sun. eternal rest. more Our sun is the central point of a system of luminaries by the side of which countless other systems exist without Human visible design or recognizable order. intelligence resists this belief, as it resists every other call to renuncia it no second alterna But first it demands a uniform picture of the world instead of a fragmentary view of this kind, and the demand springs from the natural impulse towards lightening and an impulse assisted simplifying the intellectual complexus tion, till the compulsion of fact leaves tive. in the present instance, indeed, by highly developed aesthetic and religious wants. It will be readily admitted that this picture of the universe owed no little to the contribution of the emotions and the fancy. The circular course of the divine luminaries which had been raised by the fictitious counter-earth to the sacred number ten was described as a "dance."

THE HARMONY OF THE SPHERES. rhythm of this starry dance was set to the sounds arising from the motion itself, and making unceasing music, which was recognized and known as the " harmony of the spheres." Next, the universal fire, which was the central point of the celestial procession, was known called the "mother of the by many names. gods," and so forth, but two of especially characteristic. "hearth of the its titles the "citadel It was of Zeus," may be mentioned as These were the " " altar and the The stars revolved round the universe." sacred source of all life and motion like worshippers round an altar, and the universal hearth was the centre of the world or cosmos as a man s domestic hearth was honoured as the sacred centre of his home, or as the flame that burned and was never extinguished in the civic hearth of the Prytaneum formed the holy rallying-point of every Greek community. Hence streamed the rays of light and heat, hence the sun derived his beams and communicated them again to both earths and to the moon, just as the mother of the bride lighted at a Greek wedding the fire of the new home from the parental hearth, or as a new colony would borrow its fire from the hearth of the mother-city. All the threads of the Greek view of life are combined here. We see the exalted joy in existence, the loving awe for the universe ruled by divine forces, the sublime sense of beauty, symmetry, and harmony, and not least the comfortable affection for civic and domestic peace. Those, then, who held these views, and whose universe was sur rounded by the fire-circle of Olympus as by a strong wall, found in it their home, their sanctuary, and the type of their art. Nowhere else do we find a picture of the uni verse at once so genial and so sublime. The emotional faculties, then, were satisfied in a wonderful truly degree, though at the cost of the intel lect. We have now to estimate the price which reason had to pay, and which will be found to have been by no means 2. Even the dreams of the Pythagoreans con modicum of truth or, where that modicum was wanting, there was at least an indication given of the road exorbitant. tained a " " which would ultimately lead to truth. At first sight, for

instance, no doctrine could appear of the harmony of the spheres. more arbitrary than that It obviously sprang in the from an aesthetic demand which was formulated Our eyes are filled with the grandest sights as follows how is it, then, that the twin sense of our ears should go which the answer rested was empty ? But the premise on not wholly unreasonable. For unless the space in which the fills it must stars revolve is completely void, the matter that are in themselves capable of being undergo vibrations which meaner no philosopher than Even in recent times, heard. of founder the von embryology, has Karl Ernst Baer, great last resort ; : asked if there is not " perhaps a murmur in universal space, a harmony of the spheres, audible to quite other ears than ours." Now, it was objected to the Pythagoreans that we but they deprecated cavillers of the astonishment by the following happy the blacksmith, they said, is deaf to the con do not actually hear such sounds analogy. ; A tinuous, regular beat of the hammers in his workshop ; and herein they anticipated the teaching of Thomas Hobbes, who argued that the operation of the senses depends on a change in the stimuli ; the stimulation must be interrupted, There was nothing fanciful or altered in degree or kind. the Pythagorean doctrine except only the belief that the differences of velocity in the movements of the stars were capable of producing a harmonious orchestration and in not merely sounds of varying pitch. At this point their artistic imagination had a freer rein, inasmuch as they were completely unable to determine the relative distances of the planets and the absolute velocities that ensued from them, though they could arrive, approximately at least, at the circular segments which the planets described in a given time in other words, at the angular velocities of their movements. But here, too, we shall presently find ourselves ready We have to remember that to mitigate our judgment. the premise of law and order, as pervading the universe, could hardly have been applied by the Pythagoreans to any other relations than those of geometry, arithmetic, and music the last named because of the importance of

"ALL NUMBER AND HARMONY." acoustics in their natural philosophy. and harmony were ascribed They neither knew nor IIQ Simplicity/symmetry, indifferently to all three. divined anything of the forces which produce celestial movements, so that, even had they been acquainted with the elliptic orbits of the planets, that knowledge, we may remark, would never have satisfied their demand for order. They would not have recognized the curve as the resultant of two all Their heaven, says Aristotle, rectilinear forces. number and harmony," and we may add that a correct intuition of the highest significance was still clothed in unsuitable shape. The seekers were incapable of dis covering law where it was really in operation, and it was anyhow better to look for it where it did not exist than "is not to look for it at all. Further, the assumption that the sun shines with borrowed light may be traced in the main to the parallelism between the sun and the moon which we mentioned just now. Moreover, the homo geneous conception of the universe might conceivably have suffered if a second independent source of light had been assumed so near the centre of the world. But since they could not altogether dispense with such an assumption, they found it in the Olympus alluded to above as the girdle of the universe, containing all the elements in their The firmament of fixed stars, and unsullied beauty. the planets, derived all their light from Olympus, possibly and the sun borrowed a part of his from the same source, to make amends, we presume, for his otherwise too frequent obscurations. The porous and glass-like qualities of the sun, which enabled it to collect the rays of light and to emit them again, should be noted in this connec Next we come to the second great fiction of the that of the counter-earth. may readily follow Aristotle in believing that the sacredness of the tion. Pythagoreans We number ten played a part in this conception. But the introduction of a new luminary and its insertion between the earth and the central fire had many important conse quences, and there is no reason to doubt that this fiction of the counter-earth was recommended to its inventors as

much for the sake of its results as for the reason alleged in the information at our by the Stagirite. The lacuna us to pass definite judgment ; but disposal do not permit counter-earth was to act as a the that Boeckh s opinion screen of the central fire, so as to explain its invisibility, For the supposition that the un inhabited western hemisphere of the earth was turned towards the fire was a quite sufficient explanation. It is more probable that the counter-earth was invented partly as an ostensible cause for the eclipses of the moon which occurred so frequently as to seem to require the shadow of the counter-earth in addition to the shadow of the earth. is certainly defective. The facts of history, however, are more eloquent than the arguments. Historically considered, the theory of central fire promoted and did not retard the progress of scientific research. In less than a century and a half it engendered the heliocentric doctrine. The fantastic excre all scences of the Philolaic system fell The counter-earth was the first to go away piece by piece. the death-blow was : struck at this fiction by the extension of the geographical horizon. The foundations of the hypothetical structure built by the Pythagoreans began to give way in the fourth At that time exacter news reached century at latest. Greece of discoveries in the west and in the east. Hanno, the Carthaginian, had made his great voyage of discovery, and had passed the barrier of the Pillars of Hercules, where the Straits of Gibraltar now are, which had ranked then as the furthest limit of the Western world and afterwards the outline of was the East more shortly clearly defined by Alexander s march in India. coign of observation had been reached from which the counterearth should have been visible, and since neither the counter-earth nor the central fire, thus robbed of its last protection, came in view at that point, this portion of the Pythagorean cosmology was spontaneously shattered. Nor was this all the daily circular movement of the earth till ; A : disappeared with the fictitious centre that conditioned it, and the doctrine of rotation took the place of the theory we have described as its equivalent. Ecphantus, one of

THE COPERNICUS OF ANTIQUITY. the youngest of the Pythagoreans, taught that the earth turned on its own axis. The second step on the road to the heliocentric doctrine followed swiftly on the first. The marked increase in luminosity which the planets occasion display was first noticed in Mercury and Venus, and the true cause of the phenomenon suggested itself ally inevitably as the wandering stars occasional closer to the earth. propinquity of these Thus it was clearly impossible that they could revolve concentrically round the earth. These two nearest neighbours of the sun had plainly confessed their dependence on that luminary by the revolution they respectively accomplished in the course of a solar year. Accordingly they were the first of the planets whose movements were combined with the sun s. This was the masterly discovery of Heraclides of Heraclia on the Black Sea, a man whose powerful genius, contained in a misshapen body, was familiar with the most diverse regions of science and literature, who had visited the schools of Plato and Aristotle, and had kept up a lively intercourse with the latest Pythagoreans. But here, again, Mars likewise displayed a con there was no finality. spicuous change in his degree of brightness even to the incomplete observation which obtained in that age, and thus a link was forged to unite the two inner planets with one at least of the outer ones. Philosophy was approaching the point of view reached in later times by Tycho de Brahe, who represented all the planets with the exception of the earth as revolving round the sun, while the sun with his train of planets revolved round The last and final step was taken by the earth. Aristarchus of Samos, the Copernicus of antiquity, about 280 B.C., who completed what the astronomer from the Pontus, to whom allusion has just been made, had Eudoxus had given the clue to great intellectual achievement by his discovery that less definitely this begun. the size of the sun is considerably greater than the earth s. Aristarchus computed their relative proportion at seven to one and inadequate as this estimate was in comparison with the actual fact, it was sufficient to expose the

absurdity of setting the great ball of fire to revolve like a satellite round the small world that we inhabit. The earth had to lay down the sceptre which had recently been restored to it ; heliocentricity superseded geocentricity, and the goal was reached for which Pythagoras and his disciples had smoothed and pointed the way. As things turned it was soon to be abandoned again, and its be taken for another long series of centuries by, the immemorial delusions fostered in the name of out, however, place to religion. But it is time to return from this historical forecast to its starting-point at the old Pythagorean doctrines, and there is now nothing to prevent our resuming the thread of we dropped at the close of the last the inquiry which chapter but one.