The strong tinge of mysticism which Pythagoras had brought with him from the Orphic influences of his native land to his new home in Italy served as a wholesome corrective to this exaggerated rationalism. Every religious sect thrives better in a colony than in the mother-country, as is demonstrated in the case of William Penn and many others. The aristocratic and religious league which Pythagoras founded at Croton prospered mightily, and presently the whole of lower Italy and Sicily was covered with branches of the order. Its religious ideas, particularly that of the transmigration of souls, were not new, although they have been claimed as peculiarly Pythagorean. Orphic mysticism had adopted in precisely the same fashion the notion of the fall of the spirit and its purification by transmigrations of all kinds into the bodies of men and animals. But the earnestness with which noble-minded men lived conformably to these ideas in matters of practice and brought them into connection with the results of scientific research strongly impressed the ancient world; and the close freemasonry which linked Pythagoreans from every quarter with one another set forth an ideal of manly friendship which served as a model for the institution of the Academy and similar philosophic societies. But the too strongly marked political complexion of these Pythagorean societies contained the seed of their destruction. At the end of the sixth century and the beginning of the fifth the aristocratic principle was everywhere on the decline, and in Italy itself the Pythagoreans were attacked on democratic grounds by Xenophanes of Colophon, who ridiculed the aristocratic physical sports in which even distinguished Pythagoreans (such as Milo) indulged, and vaunted the intellectual sport of his own _Sophia_. The said wisdom, it must be confessed, was of a negative rather than a positive character. Xenophanes attacked Homer, the Bible of the ancients, in verses of fierce satire, showing the gods as there depicted to be examples of every kind of immorality. By the unparalleled vigour with which he transferred the monistic tendency of Ionic rationalism to the religious problem, he, first of all Greeks, originated the monotheistic conception of the Deity, which none of the later philosophers ventured to maintain with such unflinching boldness in face of the polytheism of the vulgar herd. To the aristocratic submission to authority in matters of belief required by the Pythagoreans this democratic philosopher opposed the prerogative of doubt, and he has consequently been lauded by the sceptics of all ages as their standard-bearer. At this stage of physical observation, indeed, doubt sets in concerning natural objects. Xenophanes discovers that the rainbow is an optical illusion. He promptly generalises in his scepticism; the sun and the other stars are nothing but fiery exhalations. This assumption will lead to further results among his Eleatic friends.