 This is not the place to summarize Plato’s description of the complex structure of the world-soul at greater length. Suffice it to say that this structure combines three features – namely, (1) the components or ingredients, of the world-soul itself, which are the essential tools for dialectic; (2) the mathematical proportions that define the structure of the world-soul; and (3) the influence that the structure of the world-soul has in turn on the observable order of the universe, such as the motion of the heavenly bodies. According to Plato, the soul itself is composed of being, sameness, and difference – i.e., three of the ‘most important kinds’ discussed in the Sophist as the objects of the philosopher’s art of combination and separation (Sph. 253b–254b). Each of the three concepts that constitute the world-soul do so in a mixture of their unchangeable and their changeable types (Ti. 35a–b): the world-soul is a combination of unchangeable and changeable being, of unchangeable and changeable sameness, and of unchangeable and changeable difference. What is the use of this strange concoction? As Timaeus points out, the combination of the eternal and temporal versions of the formal concepts allows the soul to comprehend both unchangeable and changeable objects in the world (37a–c). In other words, the soul has ‘unchangeable’ tools to identify the Forms, and ‘changeable’ tools to deal with the objects in the physical realm. By mixing together the unchangeable and the changeable versions of the formal concepts, Plato maintains the unity of the soul. In other words, there is no such thing as a world-reason – dealing only with eternal being, sameness and difference – separate from the world-soul, which is concerned with temporal and changeable things, their being, sameness and difference. Rather, there is one mental force that does both, resulting in either knowledge or firm belief. Nous and psuchê are united in the Timaeus. The ‘mixed tools’ of dialectic (once more – being, sameness, and difference) are at the same time depicted as extended ‘bands’ that provide the soul with a mathematical structure through division in a complex set of proportions (35b–36b). The portions (1 - 2 - 4 - 8 - 3 - 9 - 27) of the mixture, with further subdivisions according to the arithmetical, geometrical and harmonic means, are the proportions that demarcate the intervals in theoretical harmonics (1 : 2 is the ratio underlying the octave, 3 : 2 the fifth, 4 : 3 the fourth, 9 : 8 the major second, etc.). As these harmonic divisions suggest, the world-soul is at the same time a kind of musical instrument. No music of the spheres is mentioned in the Timaeus, but Plato seems to have in mind at least the possibility of heavenly music. The mathematical proportions are applied, in turn, to explain the order and the motions of the heavenly bodies (36b–d). For the soul-bands, divided in different proportions, form circles that are ordered in a complicated system, and in doing so they represent a geometrical model of the motions and distances of the stars revolving around the earth.