Thus the first analogy is of the double in point of number, passing from one to two in order of counting, and that which is according to power is double; that which passes to the solid and tangible is likewise again double, having proceeded from one to eight; but that of the double has a mean, as much more than the less as it is less than the greater, while its other mean Footnote 1As between 3 and 6, 4 is greater than 3 by 1/3 of 3, and less than 6 by 1/3 of 6. exceeds and is exceeded by the same portion of the extremes themselves. Between six and twelve comes the whole-and-a-half (9 = 6 + 3) and whole-and-a-third (8 = 6 + 2): turning between these very two, to one side or the other, this power (9) assigned to men an accordant and proportioned use for the purpose of rhythm and harmony in their pastimes, and has been assigned to the blessed dance of the Muses. Footnote 2There were nine Muses, and they were often conceived as dancing in company with Dionysus.
In this way then let all these things come to pass, and so let them be. But as to their crowning point, we must go to divine generation and therewith the fairest and divinest nature of visible things, so far as God granted the vision of it to men; a vision that none of us may ever boast of having received at his leisure without the conditions here laid down. And besides these requirements, one must refer the particular thing to its generic form in our various discussions, questioning and disproving what has been wrongly stated; for it Footnote 3i.e. Plato’s method of dialectic; see General Introduction. is rightly found to be altogether the finest and first of tests for the use of men, while any that pretend to be tests, without being so, are the vainest of all labors. And further, we must mark the exactness of time, how exactly it completes all the processes of the heavens, in order that he who is convinced of the truth of the statement which has been made—that the soul is at once older and more divine than the body—might believe it a most admirable and satisfactory saying that all things are full of gods, and that we have never been disregarded in the least through any forgetfulness or neglect in our superiors. And our view about all such matters must be that, if one conceives of each of them aright, it turns out a great boon to him who receives it in a proper way; but failing this, he had better always call it God. The way is this— for it is necessary to explain it thus far: every diagram, and system of number, and every combination of harmony, and the agreement of the revolution of the stars must be made manifest as one through all Footnote 4i.e. we must become aware of a single, unifying scheme of proportion running through geometrical figures and proportions (diagrams
), arithmetical proportions (systems of number
), harmonic proportions (combinations of harmony
)—corresponding to square, line and cube referred to in 991a—and the rotations of the stars. to him who learns in the proper way, and will be made manifest if, as we say, a man learns aright by keeping his gaze on unity;