This unexplained faculty, or rather inherent necessity, which implies at once a power and a limit, extends to persons as well as things. The significant word sympathy expresses it. To feel a friend's grief is to put oneself in his place, think from his standpoint and in his mood--that is, suffer with him. The fear and sympathy which condition the action of tragedy depend upon the same mental process; one's own point of view is shifted to that of another, and when the two are in harmony, and only then, the claim of beauty is satisfied, and æsthetic pleasure results. By the well-known expression of Greek philosophy, 'like is only understood by like,' the Pythagoreans meant that the mathematically trained mind is the organ by which the mathematically constructed cosmos is understood. The expression may also serve as an æsthetic aphorism. The charm of the simplest lyrical song depends upon the hearer's power to put himself in the mood or situation described by the poet, on an interplay between subject and object. Everything in mental life depends upon this faculty. We observe, ponder, feel, because a kindred vibration in the object sets our own fibres in motion. 'You resemble the mind which you understand.' It is a magic bridge from our own mind, making access possible to a work of art, an electric current conveying the artist's ideas into our souls. We know how a drama or a song can thrill us when our feeling vibrates with it; and that thrill, Faust tells us, is the best part of man. If inventive work in whatever art or science gives the purest kind of pleasure, Nature herself seeming to work through the artist, rousing those impulses which come to him as revelations, there is pleasure also in the passive reception of beauty, especially when we are not content to remain passive, but trace out and rethink the artist's thoughts, remaking his work. 'To invent for oneself is beautiful; but to recognise gladly and treasure up the happy inventions of others is that less thine?' said Goethe in his _Jahreszeiten_; and in the _Aphorisms_, confirming what has just been said: 'We know of no world except in relation to man, we desire no art but that which is the expression of this relation.' And, further, 'Look into yourselves and you will find everything, and rejoice if outside yourselves, as you may say, lies a Nature which says yea and amen to all that you have found there.' Certainly Nature only bestows on man in proportion to his own inner wealth. As Rückert says, 'the charm of a landscape lies in this, that it seems to reflect back that part of one's inner life, of mind, mood, and feeling, which we have given it.' And Ebers, 'Lay down your best of heart and mind before eternal Nature; she will repay you a thousandfold, with full hands.'